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Math Studies - IA

Extracts from this document...

Introduction

IB MATHEMATICAL STUDIES

Internal Assessment

“An investigation into the value of Ryder Cup as a reflection of the US and Europe’s comparative strength in the sport of golf.”

Peter Frederiksen Svane

St. Mary’s International School

IB Candidate Number: 000134 - 039

March 10th, 2008

INTRODUCTION

The Ryder Cup takes place every other year in September, and is supposed to determine whether Europe or the US is the best in the sport of golf. Each side is represented by twelve golf players, who get the chance to play against each other over the course of three days. Contrary to regular tournaments, the Ryder Cup is played in a match play format[1] rather than using stroke play[2]. The question therefore arises if the Ryder Cup is a true reflection of which region (US or Europe) has the best group of golfers. Are Europeans really better golfers than Americans, since they have won all the meets since the new millennium? To put a final answer to this debate, the investigation will focus on performances in regular tournaments, in which the Ryder Cup players have all competed, and their performance in the Ryder Cup. Various mathematical processes will be carried out within the scope of relevance in order to reach a conclusion to the mentioned task.

The performance of the Ryder Cup team players in regular stroke play tournaments on their seasonal tours, where the players come in direct action against each other under the same conditions, will be determined, and this will be compared and weighed in relation to the outcome of the Ryder Cup. Hence the investigation is intended to compare the results of the Ryder Cup with the Ryder Cup players’ performance in regular stroke play tournaments where they play directly against each other.

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Middle

image04.png

Hence Europe performed 1.95 better (94.7%) than the US in 2004 and 2006.

When the same is done with the processed data of the majors, the following results become apparent:

In the time up till the Ryder Cup 2002, Europe performed this amount better than US in the majors:

.                image05.png

This number shows how many times worse the US performed than Europe. This number reflects a European win because it is greater than 1.

In the seasons following up to Ryder Cup 2004, Europe performed this amount better than the US in the majors:

image06.png

Indeed, Europe actually performed .9923089048 times worse than US during this period of time by an amount of since .9923089048 < 1.

The time prior to the most recent Ryder Cup in 2006, the following comparative results between the US and Europe in the majors have been found:

image07.png

Again, Europe performed worse than the US in the majors by an amount .9932860227. Again, the number’s value less than one reflects a US win.

Now the two variables have been defined. The independent being the times better Europe performed better than US in the Majors, and the dependent being how many times greater the European victories in the Ryder Cup was. This can be represented as a scatter plot, which can assist in identifying any correlation between the two variables, and the strength between them.

GRAPH SHOWING THE RELATIONSHIP BETWEEN THE OUTCOME IN MAJORS AND THE OUTCOME IN THE RYDER CUPimage08.png

As it appears in the scatter plot with the least square regression line, the greater the European win in the Majors is the smaller their victory in the Ryder Cup is. Hence there is a negative correlation between the two variables. In other words, the better the US performs in the majors (going toward zero on the x-axis, since any value below on represents a US win)

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Conclusion

________________________________________________________________________

Word Count: 4559

APPENDICES

________________________________________________________________________

Ryder Cup players in 2002, 2004 and 2006

2002

  • USA
  • Scott Hoch
  • David Toms
  • David Duval
  • Hal Sutton
  • Mark Calcavecchia
  • Stewart Cink
  • Scott Verplank
  • Paul Azinger
  • Jim Furyk
  • Davis Love III
  • Phil Mickelson
  • Tiger Woods
  • Europe
  • Colin Montgomery
  • Sergio Garcia
  • Darren Clarke
  • Bernhard Langer
  • Padraig Harrington
  • Thomas Bjørn
  • Lee Westwood
  • Niclas Fasth
  • Paul McGinley
  • Pierre Fulke
  • Phillip Price
  • Jesper Parnevik

2004

  • USA
  • Tiger Woods
  • Phil Mickelson
  • Davis Love III
  • Jim Furyk
  • Kenny Perry
  • David Toms
  • Chad Campbell
  • Chris DiMarco
  • Fred Funk
  • Chris Riley
  • Jay Haas
  • Stewart Cink
  • Europe
  • Paul Casey
  • Darren Clarke
  • Luke Donald
  • Sergio Garcia
  • Padraig Harrington
  • David Howell
  • Miguel Angel Jimenez
  • Thomas Levet
  • Paul McGinley
  • Colin Montgomery
  • Ian Poulter
  • Lee Westwood

2006

  • USA
  • Tiger Woods
  • Phil Mickelson
  • Jim Furyk
  • Chad Campbell
  • David Toms
  • Chris DiMarco
  • Vaughn Taylor
  • J. J. Henry
  • Zach Johnson
  • Brett Wetterich
  • Stewart Cink
  • Scott Verplank
  • Europe
  • Darren Clarke
  • Paul Casey
  • Luke Donald
  • Sergio Garcia
  • Padraig Harrington
  • David Howell
  • Robert Karlsson
  • Paul McGinley
  • Colin Montgomery
  • José Maria Olazabal
  • Henrik Stenson
  • Lee Westwood


[1]“Play in which the score is reckoned by counting the holes won by each side.” 5th February, 2008: http://dictionary.reference.com/browse/match%20play>

[2]“Golf competition in which the total number of strokes taken is the basis of the score.” 5th February, 2008: http://dictionary.reference.com/browse/stroke%20play

...read more.

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